A graphing calculator is needed to complete this section.

In this section, you will be solving square root equations using graphs.

There are two methods that can be used to solve a square root equation using its graph. 

Method 1 - Solving by a Square Root Equation by Graphing Both Sides

flow chart with the following steps Step 1 - Graph each side of the equation as a separate function; Step 2 - Find the point of intersection * This is where the two functions are equal. * If the graphs do not intersect, then there is NO solution; Step 3 - The x-coordinate of the point of intersection is the solution

Solve √3x − 2 for x. Follow along on your calculator.

  1. Graph each side of the equation as a separate function.

    y = √3x − 2 and y = 5

    graph of the equations y equals the square root of the quantity 3x-2 and y=5

  2. Find the point of intersection of the two functions - INTERSECT option, 2nd Trace #5.

    In order to "see" the point of intersection you may have to enlarge the viewing window by adjusting the WINDOW setting or ZOOM (#2 Zoom IN – Enter twice to activate)

    graph of the equations y e <body> quals the square root of the quantity 3x-2 and y=5 with intersection at (9,5)

  3. Find the x-coordinate of the point of intersection.


    The point of intersection is at (9, 5). So, the solution to the equation is x = 9.

    Click here for extra practice.

Method 2 - Solving by a Square Root Equation by Finding a Zero

flow chart with the following steps: Step 1 - Set the equation equal to 0; Step 2 - Graph the side of the equation that contains the radical; Step 3 - Find the zero (x-intercept); The x-value is the solution

Example √3x − 2 = 5 for x. Follow along on your calculator.

  1. Set the equation = 0.
    √3x − 2 = 5 (Subtract 5 from both sides)
    √3x − 2 − 5 = 5 − 5 (Simplify)
    √3x − 2 − 5 = 0
  2. Graph the side that contains the radical. (You may need to adjust your viewing window.)
    ♦ Rewrite the equation and put the constant before the radical.

    -5 + √3x − 2 = 0 Screen shots of graphing calculator screens showing a table and graph of Y1=-5 + the square root of the quantity 3x-2

  3. Find the zero (x-intercept).
    graphing calculator screen showing the graph of y=-5 + the square root of the quantity 3x-2 with the x-intercept at x=9The solution is zero → so x = 9

Both methods yield the same solution: x = 9.

Click here for extra practice.